Question

A triangle is formed between Bob and 2 lampposts. The distance from Bob to one lamppost is 25 feet, and the distance from Bob to the other lamppost is 30 feet. The distance between the 2 lampposts is 20 feet.

Bob is standing 25 feet from a lamppost that is to his left and 30 feet from a lamppost that is to his right. The distance between the two lampposts is 20 feet. What is the measure of the angle formed from the line from each lamppost to Bob? Approximate to the nearest degree.

1. 202 = 252 + 302 − 2(25)(30)cos(A)

2. 400 = 625 + 900 − (1500)cos(A)

3. 400 = 1525 − (1500)cos(A)

4. −1125 = −(1500)cos(A)

degrees

Answer 1

41 degrees

Explanation:

i just know

Answer 2

41 degrees

Explanation:

see the attached figure to better understand the problem

we know that

Applying the law of cosines

`a^2=b^2+c^2-2(b)(c)cos(A)`

we have

`a=20\ ft\\b=30\ ft\\c=25\ ft`

A is the measure of the angle formed from the line from each lamppost to Bob

substitute

`20^2=30^2+25^2-2(30)(25)cos(A)`

`400=900+625-(1,500)cos(A)`

`400=1,525-(1,500)cos(A)`

`(1,500)cos(A)=1,525-400`

`(1,500)cos(A)=1,125`

`cos(A)=(1,125)/(1,500)`

`A=cos^(-1)((1,125)/(1,500))=41^o`